1. Field of the Invention
The present invention relates generally to methods and systems of quantifying uniformity of measured quantities on semiconductor wafers, and more particularly, to improved methods and systems for characterizing and analyzing nonuniformities on semiconductor wafers and providing feedback and control to preceding semiconductor manufacturing processes.
2. Description of the Related Art
Semiconductor wafers undergo numerous processes during the semiconductor manufacturing process. Layers may be added, patterned, etched, removed, polished and many other processes. After each process the wafer is typically examined to confirm the previous process was completed with an acceptable level of errors or nonuniformities. The various operating variables (e.g., event timing, gas pressure, concentrations, temperatures, etc.) of each process the wafer is processed through are recorded so that any changes in any variable may be quickly identified and potentially correlated to any errors or nonuniformities discovered when the wafer is examined.
FIG. 1A shows a typical etched wafer 100. A top layer of material was mostly removed from the wafer in the etch process except for a portion 106 of the top layer. For clarity purposes, the portion 106 is a portion of a layer or ultrathin film. A notch 104 is typically included in each wafer 100 so that the wafer can be oriented (aligned) in the same position during the various manufacturing processes. The portion 106 is a nonuniform portion of the surface of the wafer 100 and therefore can be termed a nonuniformity. As shown, the portion 106 is in the approximate form of a ring or annular shape where the top layer was removed from the center and around the edges of the wafer 100.
FIG. 1B shows another typical etched wafer 120. A portion 108 of a top layer remains, when the top layer was mostly removed in the etch process. The portion 108 is typically termed an azimuthal-type nonuniformity on the surface of wafer 120 because the nonuniformity 108 is not the same at the same radius around the wafer 120.
Prior art approaches to describing nonuniformities 106, 108 include subjective, verbal descriptions such as xe2x80x9ccenter-fastxe2x80x9d for annular nonuniformity 106 or xe2x80x9cleft side slowxe2x80x9d for azimuthal nonuniformity 108. Center-fast generally describes wafer 100 because material from the center of the wafer 100 is removed faster than the material in the annular region 106. However, center-fast does not provide a specific, objective and quantitative description of the nonuniformity 106. Similarly, left side slow describes wafer 120 because the etch process removed material from the left side region 108 slower than the other regions of the wafer 120 but left side slow also fails to provide a specific, objective and quantitative description of the nonuniformity 108.
The descriptions of the nonuniformities 106, 108 are used to provide feedback to correct errors and inconsistencies in the etch and other preceding processes that were performed on the wafers 100, 120. The descriptions of the nonuniformities 106, 108 can also be used to track the impact of the nonuniformities 106, 108 on subsequent semiconductor manufacturing process and on metrics from completed semiconductor devices (e.g., device yields, performance parameters, etc.)
As nonuniformities become smaller and smaller, the nonuniformities become less symmetrical and also more difficult to accurately describe with the subjective, verbal descriptions. FIG. 1C shows a typical wafer 150 with multiple, asymmetrical nonuniformities 152A-G. The nonuniformities 152A-G can be smaller and are less symmetrical than nonuniformities 106, 108 in part because the various variables in the etch and other previous processes are very stringently controlled. The subjective, verbal descriptions have therefore become insufficient to accurately describe the nonuniformities 152A-G so that further improvements in the preceding processes can be successfully completed.
A more objective description of wafer uniformity is referred to as a 3-sigma uniformity metric. The 3-sigma uniformity metric quantifies a standard deviation of measurements of some quantity of the wafer. By way of example, the 3-sigma can be an expression of the deviations in thickness of the wafer detected by an array of measurement points across the wafer. FIG. 1D shows a typical 49-point array used in completing a scan of wafer 160. The thickness of the wafer 160 is measured at each of the 49 points. The 49-points are arranged with a center point 162, and three concentric rings 164, 168, 172. The inner ring 164 has 8 evenly spaced points. The intermediate ring 168 has 16 evenly spaced points. The outer ring 172 has 24 evenly spaced points. The rings 164, 168, 172 are typically approximately equally spaced radially from the center point 162. Each of the points in the rings 164, 168, 172 and the center point 162 is typically assigned to represent a given portion of the wafer 160. For example, a typical wafer 160 has a 3 mm edge exclusion zone on the outer perimeter of the wafer 160. The rings 164, 168, 172 and the center point 162 are spaced equidistant and therefore each of the 49 points represent about {fraction (1/49)}th of the area of the wafer 160, less the 3 mm exclusion zone (i.e., the outer edge of the wafer where expected process abnormalities occur). Because nonuniformities do not suddenly appear under a single scan point, the nonuniformities are automatically smoothed due to the choice of measuring points.
The measured thicknesses can be correlated to other aspects of the wafer such as an etch rate at the particular measured point A standard deviation (SD) and mean of the etch rates at these 49 points are determined. The 3-sigma nonuniformity metric equal to [3*(SD)/mean]/100, expressed as percentage is typically reported. The 3-sigma metric effectively compresses or summarizes all of the individually measured point etch rates to one summary value. However, the 3-sigma metric does not provide any information about the relationship between the etch rates at the different measured points. This relationship can become important when higher uniformity is achieved. The relationship can help identify differences between different etch patterns with the same 3-signal nonuniformity metric.
Many prior art approaches apply a Fourier or a Bessel decomposition on the measured data to better describe a shape and magnitude of the nonuniformity 106, 108, 152A-G. However, Fourier and Bessel decompositions are an effort to force-fit the shape of the nonuniformity to a predetermined Fourier and Bessel defined shape, rather than determine the actual shape of the nonuniformity 106, 108, 152A-G. The Fourier and Bessel decompositions are therefore only estimating the magnitude of the nonuniformity in the forced-fit shape. While the Fourier and Bessel decompositions provide additional objective descriptions of the nonuniformities, the Fourier and Bessel decompositions still do not accurately describe either the shape or the magnitude of the nonuniformity 106, 108, 152A-G.
In view of the foregoing, there is a need for an improved system and method of objectively and accurately quantifying a nonuniformity and correlating the nonuniformity to a any relevant change in the system (for e.g. process variable, hardware change).
Broadly speaking, the present invention fills these needs by providing a system and method for quantifying a nonuniformity and correlating the nonuniformity to process variables. It should be appreciated that the present invention can be implemented in numerous ways, including as a process, an apparatus, a system, computer readable media, or a device. Several inventive embodiments of the present invention are described below.
One embodiment includes a method for determining a multiple uniformity metrics of a semiconductor wafer manufacturing process includes collecting a quantity across each one of a group of semiconductor wafers. The collected quantity data is scaled and a principal component analysis (PCA) is performed on the collected, scaled quantity data to produce a first set of metrics for the first group of semiconductor wafers. The first set of metrics including a first loads matrix and a first scores matrix.
Collecting the quantity across each one of the first group of semiconductor wafers can include measuring a quantity at several locations on each one of the first group of semiconductor wafers and storing the measured quantity values in a matrix of the first group of semiconductor wafers and the locations.
Scaling the collected quantity data can include subtracting a pre-selected value from the measured quantity values. Scaling the collected quantity data can also include subtracting a mean value of the measured quantity values for a selected wafer from the measured quantity values of the selected wafer.
The first loads matrix can include a first set of principal components present in the collected, scaled quantity data. The first scores matrix can include a first set of scores. Each of the first set of scores provides information relating a contribution magnitude for each of the principal components.
The method can also include determining a first subset of significant loads from the first set of loads.
Determining the first subset of significant loads from the first set of loads can include providing a noise level of semiconductor wafer manufacturing process and a confidence level. A confidence factor that correlates to the confidence level is determined. A significant level of scores equal to a product of the confidence factor and the noise level is calculated. The significant level of scores correspond to a significant number of components. The first subset of significant loads are identified as the loads from the first set of loads that have the significant number of components.
Alternatively, determining the first subset of significant scores from the first set of loads includes generating a noise vector and determining a set of projected noise scores. The set of projected noise scores arc recorded. A multiple of projected noise iterations is selected and performed. A mean and standard deviation of the projected scores is determined. The standard deviation of the projected scores is stored and a subsequent noise level is selected. A multiple of subsequent noise level iterations is selected and performed. A standard deviation of the noise level is calculated and graphed. A confidence factor that correlates to the confidence level is calculated. The significant level of scores correspond to a significant number of components. The first subset of significant loads are identified as the loads from the first set of loads that have the significant number of components.
A selected process variable can be changed and a quantity data for a second group of semiconductor wafers are collected. The collected quantity data for the second group of semiconductor wafers can be scaled. The second set of scaled data can be projected on the first subset of significant loads to identify a set of projected scores. The second set of projected scores can be analyzed.
Analyzing the second set of projected scores can include correlating the selected process variable with the second set of projected scores.
Analyzing the second set of projected scores can also include identifying a set of difference components included in the second set of projected scores that are not included in the first set of projected scores. The set of difference components can include one or more new components.
Correlating the selected process variable with the plurality of projected scores can include performing partial least squares (PLS).
The first loads matrix can be an orthonormal matrix. The first scores matrix can be an orthogonal matrix. The quantity data can include etch rate data.
Substantially all of the process variables in the semiconductor wafer manufacturing process are substantially, constant during a processing of the first group of semiconductor wafers.
Another embodiment includes a method for determining uniformity metrics of a semiconductor wafer manufacturing process that includes collecting a quantity across each one of a first group of semiconductor wafers and scaling the collected quantity data by subtracting a pre-selected value from the measured quantity values. A principal component analysis (PCA) can be performed on the collected, scaled quantity data to produce a first set of metrics for the first group semiconductor wafers. The first set of metrics includes a first loads matrix and a first scores matrix. A first subset of significant loads can be determined from the first set of loads. The quantity data can include etch rate data.
Another embodiment includes a method for correlating a nonuniformity to a process variable includes collecting a quantity across each one of a first group of semiconductor wafers and scaling the collected quantity data. A principal component analysis (PCA) is preformed on the collected, scaled quantity data to produce a first set of metrics for the first group of semiconductor wafers. The first set of metrics include a first loads matrix and a first scores matrix. A subset of significant loads is identified from the first loads matrix. A selected process variable is changed and quantity data is collected for a second group of semiconductor wafers. The collected quantity data for the second group of semiconductor wafers is scaled. The second set of scaled data can be projected on the first subset of significant loads to identify a set of projected scores. The selected process variable can be correlated to the set of projected scores. The quantity data can include etch rate data.
Another embodiment can include a system for quantifying uniformity pattern and determining a correlation between a process variable and a nonuniformity on a semiconductor wafer. The system includes a scanning device that has the capability of measuring a quantity at multiple locations of each one of a set of wafers. A database that includes multiple process variables and the measured quantities at corresponding locations for each one of the wafers. The database is coupled to the scanning device.
A processor is also coupled to the database. A logic that determines a set of uniformity metrics of a semiconductor wafer manufacturing process for a first set of semiconductor wafer and a second set of semiconductor wafers. The system also includes a logic that correlates a nonuniformity to a process variable.
The present invention provides more specifically defined uniformity metrics that can be correlated to process variables. Correlating process variables to the uniformity metrics allows for improved troubleshooting and refinement and improvement of the semiconductor manufacturing processes.
Other aspects and advantages of the invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, illustrating by way of example the principles of the invention.